Bernoulli Equation
In an ideal inviscid, incompressible flow, we have, by conservation of energy,
![$\displaystyle p + \frac{1}{2}\rho u^2 + \rho g h =$](http://www.dsprelated.com/josimages_new/pasp/img3072.png)
![\begin{eqnarray*}
p &=& \mbox{pressure (newtons/m$^2$\ = kg /(m s$^2$))}\\
u &=...
...\
\mbox{\lq\lq Inviscid''} &=& \mbox{\lq\lq Frictionless'', \lq\lq Lossless''}
\end{eqnarray*}](http://www.dsprelated.com/josimages_new/pasp/img3073.png)
This basic energy conservation law was published in 1738 by Daniel Bernoulli in his classic work Hydrodynamica.
From §B.7.3, we have that the pressure of a gas is
proportional to the average kinetic energy of the molecules making up
the gas. Therefore, when a gas flows at a constant height , some
of its ``pressure kinetic energy'' must be given to the kinetic energy
of the flow as a whole. If the mean height of the flow changes, then
kinetic energy trades with potential energy as well.
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Bernoulli Effect
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Pressure is Confined Kinetic Energy